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lockwo / quantum_computation

Code for implementing and experimenting with quantum algorithms
MIT License
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having problem in deriving the upper bound mentioned in the paper proof of theorem 1 #3

Open kotoriii272 opened 1 month ago

kotoriii272 commented 1 month ago

Hi lockwo, it has beem very inspiring to watch your vedios on the noise induced barren plateau problem. While I'm learning this paper, it is quite hard to me to derive this equility in the Supplementary Note 2 - Proof of Theorem 1 : CodeCogsEqn (1)

, I have no idea about how the W and V are producted together here. I would be very grateful if you can spend some of your time helping me with this issue.

lockwo commented 1 month ago

W here is a quantum noise channel, so that is just the operation for the noise channel application

kotoriii272 commented 1 month ago

W here is a quantum noise channel, so that is just the operation for the noise channel application

Thanks a lot lockwo. But I'm still a bit confused about what the a(L, j) stands for

lockwo commented 1 month ago

a is the Pauli coefficient that represents the expected value, see eq 45. L is just the layer and j is qubit index